Thoughts on processes

Tom, Eduardo and I are working on a paper on autonomy, hopefully to be presented at ECAL. We wanted a definition of autonomy that would be something along the lines of “homeostasis of a recursive network of processes” or “homeostasis of relations between processes” that could be applied to both real living systems and to artificial systems, so that we can say how far various approaches to ALife can get towards creating artificial autonomy. However, this definition relies on understanding what we mean by a “process” in a physical or artificial system.

This is the result of an email discussion with Tom and Eduardo and is my attempt to grasp towards such an understanding. I’m putting it on the blog in the hope that it will generate some useful discussion. The question was whether a CTRNN or other evolutionary robotics style agent can be said to be autonomous in this sense of being a homeostatic network of processes – in a way the point of this is to argue for a negative answer to this question, but it touches on a lot of other topics on the way, especially the importance of thermodynamics for modelling autonomy. It’s quite unstructured and is presented in an odd style but hopefully there’s enough here to start a good discussion.

Nathaniel Virgo

In a physical system it is usually easy to point to processes and identify them. This should form the starting point for developing our intuitions about what the word “process” means. Examples of processes in a candle flame are convection and combustion; in a tornado we have the transfer of heat energy from the sea to the air, the condensation of water vapour as humid air rises in the eye etc.; in a living cell the processes are conversion of compounds by enzymes, RNA transcription, photosynthesis, the switching on and off of genes depending on chemical concentrations etc. It might be useful to come up with some more examples.

It’s harder to identify “relations between processes” in physical systems, but perhaps we could say that the relations between the processes in a flame are that combustion provides the heat for convection while convection increases the oxygen available for combustion — a circular network. Also, the process of wax melting due to the heat and the using up of wax due to combustion sustain a fourth process, the drawing of hot wax up the wick, which sustains combustion – see figure 1.

There are “epiphenomenal” (but unavoidable) processes in a candle flame, such as the production of smoke. There are also processes that must take place but which are not dependent on the flame, such as the manufacture of candles and the production of oxygen by the biosphere. This is also true of living things, however, since all life ultimately depends on processes of nuclear fusion in the sun which are not affected by life on Earth.

In a CTRNN it is not so easy to identify processes. In fact I can’t think of a way to do it at all, although that’s not to say there isn’t one. It may be that in the analysis of a specific CTRNN evolved for a specific task one can identify things that would naturally be called processes — I’m not familiar enough with that kind of work to say. What we need, though, is not an attempt to define “process” in such a way that all CTRNNs trivially have them, but an example of something that would unequivocally be called a process in natural language. If anyone can think of something like that it would be great.

The point of this exercise is not to say that all processes must be physical processes but to ask what it is about physical processes that makes us call them processes. This train of thought might lead us to consider whether there are important constraints in the physical world that are necessary for processes to exist, which we can abstract into artificial worlds. This would be a logical requirement rather than a metaphysical one.

Figure 1 looks like a diagram representing a CTRNN but the resemblance is superficial. In a CTRNN diagram the nodes represent single variables whereas in this diagram the whole process is supposed to be represented by the node: not just a single real variable but the character of what happens in the process, such as the oxidisation of wax molecules to release heat energy in a flame or the organisation of air into a circularly moving column in a tornado.

All the physical processes that I have identified have a thermodynamic character. Perhaps this is not important but I suspect it is. Processes seem to be those things which cannot take place without energy being converted from one form into another, and thus they are the things to which the second law of thermodynamics applies (indeed, non-equilibrium thermodynamics is referred to as “the theory of irreversible processes”). I think this is an important clue to what kind of constraints need to be in place for non-trivial autonomy to be implemented. In a too general artificial world (or relational/logical description of the world) there is nothing to stop a process from just doing something without having to use something else up. Real processes necessarily produce waste products that must be re-used or disposed of, and they inevitably produce entropy (heat), meaning that they cannot run indefinitely without a supply of resources.

There’s also the statistical nature of physical processes, which is closely related to their thermodynamic nature. The physical processes I’ve identified are macroscopic descriptions that apply only probabilistically to microscopic physical entities. For instance, convection in a flame means that on average gas molecules are moving up through the flame, but some of them could be moving downwards against the flow (or they could all move downwards for a short period of time) and convection would still be taking place. Combustion is the oxidisation of wax molecules, but all chemical reactions take place in both forward and reverse directions (because the laws of physics are invariant under time reversal), so a few of the oxidised molecules will be turning back into wax and returning oxygen molecules to the air — it’s just that this happens infinitesimally more slowly than the forward process and so on average the reaction happens in a particular direction. In other words, processes are constraints on what happens to the microscopic state of the system. I’ve written in other emails (and will eventually post on this blog) about the importance of seeing structure in terms of constraints on the microscopic state, and I think it might be important to see processes in this way as well.

The rates at which the processes take place in a candle flame are dynamically stable. For example, less convection would result in a build-up of hot air at the bottom of the flame due to combustion, resulting in increased convection, whereas a greater than normal rate of combustion would presumably make the combustion less efficient somehow or use up the wax that had been drawn up the wick, resulting in less heat being produced and therefore less convection. In this sense there is a correspondence between physical systems and dynamical systems, because we’re creating a dynamical system with variables representing something about the processes (in this case their rates) and then looking at an attractor of that dynamical system. (whether to call this homeostasis is an open question)

However, it’s important to realise that creating a model of the system in this way would not be possible if the system was not there. The rate of convection taking place in the flame is not meaningful if there is no flame. One could say the flame itself creates the variables that it maintains, although I’d say that’s a little grandiose. Perhaps this point is easier to see in Varela et al’s cellular automaton model of autopoiesis. Let’s say that it maintains homeostatically the ratio between its volume and its surface area (I don’t know if it does as I haven’t read the papers but it’s sure to maintain something of that sort or it would grow indefinitely). We could model this with a dynamical system that has variables for the volume and surface area of the organism, but if the organism disintegrated into a disorganised collection of grid cells these variables would no longer have any meaning: the volume and surface area of the organism are meaningless unless there is an organism.

There is also the point that it’s not just these variables that are being maintained, it is also the shape of the system itself. The dynamical system representing a flame is locally stable partly because of the way the flame is structured, and a (smallish) perturbation to that structure (perhaps caused by a slight breeze) will be corrected.

It’s also worth noticing that there are things in the Varela et al model that it does seem natural to call processes, such as the maintenance of the membrane. For this and the reasons above I think that perhaps all processes are things that are distinguished on a higher level than the one on which it takes place (eg. Physical processes are not distinguished on the atomic microstate level but at the macroscopic “phenomenological” level). I’m tempted to introduce a new term to mean the things on the lower level on which processes operate (perhaps “atoms,” although I don’t mean necessarily physical atoms. The word “substrate” is attractive as well). As another way to get at this distinction, consider again our dynamical model of the rates of processes in a flame. If we only had access to the equations of this model and did not know what they represented I suspect it would be very difficult if not impossible to say what processes were taking place. This is because the processes do not take place in the model, they take place in the flame. The model abstracts them away, so it only has variables and the relationships between them and does not include the processes that cause those relationships.

For these reasons I suspect that the reason that I cannot identify processes in a CTRNN is that CTRNNs are modelled on too high a level to have processes.

CTRNNs also lack the properties of flames and of Varela et al’s model that the variables that can be used to represent the system become meaningless if the system disintegrates and that the structure of the system is maintained. This is also because they are modelled on too high a level for this to be possible. In a CTRNN the variables are part of the system itself whereas in a flame (or a cell) they arise from the system’s structure, which is determined by the system.

Tom Froese had a useful response to this, along the lines that when we do evolutionary robotics we assume the existence of an autonomous system (in the sense being developed here, in which the system consists of processes that conspire to keep those same processes maintained), but we abstract that away and model only the dynamics of (some of) those processes. However, because of the level of abstraction these processes are by definition viable until we decide to end the test run. Evolutionary robotics is therefore a useful method for investigating some aspects of autonomous systems (structural coupling and dynamical behaviour) but can never result in the evolution of a system that is autonomous in its own right.

Perhaps an interesting addition to this method would be to add ‘thermodynamic’ constraints on these dynamics, i.e. to include a little bit of physics in the model. In other words, include some information in the model about what sort of things the nodes represent and how energy flow affects their dynamics. This will not get us all the way to genuine autonomy, however, as we would still be pre-defining the agent’s identity. (I would guess that the reason this doesn’t tend to be done is that the CTRNN is supposed to represent the agent’s control system, which is assumed to be supported by a further network of metabolic processes that are not modelled, so it’s dynamics are relatively unconstrained by physics)

Maintaining an evolutionary robotics agent’s dynamics within a bounded region is a useful metaphor for an autopoietic system’s maintenance of its structure (and it certainly seems to be useful in practical terms) but we should be very cautious about claiming that they are the same thing, since the autopoietic system distinguishes itself as a unity whereas the unity-ness of an evolutionary robotics agent is presupposed.

Could something with the properties of autonomy that we’re looking for arise within the dynamics of a CTRNN or other control system, distinguished on a higher level than the variables that define the CTRNN? The answer here has to be “maybe,” but it doesn’t seem relevant to evolutionary robotics as it’s currently done. If this were to happen it would not be the ‘agent’ itself that had these aspects of autonomy but some other thing that’s able to distinguish itself from an environment within the combined ‘agent’/’environment’ system. Aiming towards this would require a shift in perspective towards evolving a substrate rather than an agent, and this would take us beyond what I mean here by “evolutionary robotics.”

Finally, a general point about the importance of thermodynamic constraints, which was suggested to me in an email from Eduardo. We’re all convinced of the importance of space and time and of not abstracting them away as in GOFAI models. Thermodynamics is an aspect of our physical world that’s arguably as fundamental as space and time, and perhaps by including it in our models we will gain as much insight as we do by including space and time.

9 Responses

Thanks for this Nathaniel! As you already know I generally agree with your claims, so I’ll limit this comment to your last point. What I want to consider is the role of abstraction in the various approaches to AI, which perhaps could roughly be treated as follows:

Why do I claim that CTRNNs abstract space? It is because there seems to be no clear sense in which we could speak of the distance between two nodes making an operational difference to their interactions. Thus, there are no spatial relations which could have an impact on the systems dynamics.

Perhaps the lack of processes and thermodynamics in CTRNNs could in this manner be understood as particular symptoms of a general lack of spatial embeddedness. Thus, after the shift of GOFAI to CTRNNs, which made time concrete, there seems to be a need for a further shift to spatially embedded networks which also makes space concrete. It appears that such a shift is a necessary requirement for artificial life research into the mechanisms underlying autonomy to progress.

Broadly I think I agree with that point, but adding spatial embeddedness to CTRNNs won’t automatically give them processes or thermodynamics — after all there are already spatially embedded variations on the CTRNN theme, such as GasNets, but these don’t necessarily have processes or thermodynamic constraints (having said that, GasNets do model the process of diffusion, but there are still aspects of their dynamics which are not identifiable as being the result of a particular process. In any case I don’t think it’s because they’re spatial that there’s a process involved, and certainly you can have a spatial model with no thermodynamic constraints).

While CTRNNs themselves are not spatially embedded, they are usually situated in bodies that are free to move in some way in space — that’s what I meant by not abstracting away space in evolutionary robotics.

But if we were to have an artificial autonomous unity I do think it would probably have to be spatially embedded in the way you’re suggesting (although perhaps with a very loose definition of space), otherwise it would be hard for there to be a way for it to be distinguished from its environment.

In an autonomous unity in the physical world such as an organism, all process need a supply of free energy in order to continue, which must be supplied by something in the environment or by another process. For instance, neuron firing in the brain (as I understand it) requires the molecule ATP, which is ultimately produced by digesting food. In a GASNet, or an ordinary CTRNN, there is no such consideration of energetics as the control system is assumed to be supported by some power source that is external to it.

To clarify, I don’t think this is a problem with GASNets or CTRNNs per se, it’s just that if we wanted to model the autonomy of a whole organism it would mean modelling the whole metabolism and not just the control system, and so in that case we’d have to include considerations of free energy, its eventual degradation into heat and the associated production of entropy. However, I have an intuition that adding some of these types of consideration to things like CTRNNs would produce useful insights, although it would take a bit more work to say exactly how this could be done.

I’ve read the original posting from Nathaniel and the subsequent discussion with interest – thanks. I would like to add a few comments from an Artificial Chemistry perspective, especially in relation to ‘metabolism first’ theories of the Origin of Life. I’m not sure how much overlap there is between Neural Networks and Artifical Chemistries (ACs), but ACs are certainly networks, and a key motivation for studying them is to understand the nature of the processes that can take place in the networks.

Thermodynamics is certainly important for modelling chemistry, as is ensuring mass conservation. Both place important constraints on the structure and behaviour of the network. My thoughts on including thermodynamics in Artificial Chemistry models are at http://www.simsoup.info/SimSoup/News_2006.html.

Much of the attention in Origin of Life research has focused on how ‘smart’ molecules such as RNA could have originated. The reason for this is that such template replicating molecules are often thought to be essential for inheritance, and therefore for evolution.

The problem with this is that smart molecules are spectacularly unlikely. I think that what is needed is less focus on smart molecules, and more focus on understanding the nature and dynamics of chemical processes, especially cycles, that can take place in chemistries made up of ‘dumb’ molecules. Such cycles are (and have to be) driven by externally provided energy. They are, in effect, mechanisms that maintain themselves by producing entropy. The view I am taking is that a chemical cycle is an attractor, and to some extent can be regarded as a ‘thing in itself’ or a ‘network entity’. Under metabolism first theories, it would be the chemical cycle itself that would carry inherited information and be capable of evolution. The detail of how this could work is well documented, so I won’t won’t go into it here.

The development of smart molecules would not be essential for the Origin of Life, but an evolving process/attractor/’network entity’ would provide an excellent environemt within which smart molecules could develop; a molecule that could do something ‘useful’ in the process would be selected for.

So what I am saying overall?:-

* I’m supporting much of what has been said already…
* Making some links with Artificial Chemistry…
* And making the case for network thinking. Maybe it is the process / ‘network entity’ as a whole and the relationships between its nodes that is ‘smart’, rather than the individual nodes.